cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A112530 Numbers k such that prime(k) +/- k and prime(k) +/- 2k are all primes.

Original entry on oeis.org

720, 1920, 5580, 14370, 17160, 21090, 26040, 28560, 38280, 43680, 43890, 50730, 60090, 77850, 100800, 104760, 120060, 125190, 155100, 167850, 171780, 193260, 202470, 206460, 211860, 217830, 221880, 224070, 249900, 249990, 252420, 261960
Offset: 1

Views

Author

Zak Seidov, Sep 10 2005

Keywords

Comments

Are all terms divisible by 30?
Union of A064403 and A112529.

Links

Crossrefs

Cf. A064403, A112529.

Programs

  • Mathematica
    Select[Range[720, 2000000, 10], PrimeQ[Prime[ # ]+# ]&&PrimeQ[Prime[ # ]-# ]&&PrimeQ[Prime[ # ]+2# ]&&PrimeQ[Prime[ # ]-2# ]&]
Select[Range[262000],AllTrue[Prime[#]+{#,-#,2#,-2#},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 02 2021 *)

A143794 Primes p, with index k, such that p-k and p+k are both prime.

Original entry on oeis.org

7, 13, 61, 181, 317, 827, 1831, 2657, 2801, 3181, 3739, 4093, 4561, 5011, 5443, 5531, 5653, 6359, 6659, 9029, 10729, 11383, 13109, 13907, 14489, 15217, 15859, 16603, 17581, 20393, 21499, 23537, 25037, 25169, 26153, 26959, 27077, 27803, 27851
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Sep 01 2008

Keywords

Examples

			7 = prime(4) and both 7 - 4 = 3 and 7 + 4 = 11 are prime;
13 = prime(6) and both 13 - 6 = 7 and 13 + 6 = 19 are prime;
61 = prime(18) and both 61 - 18 = 43 and 61 + 18 = 79 are prime.

Links

Crossrefs

Cf. A064403 (corresponding prime indices).

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[p-n]&&PrimeQ[p+n],AppendTo[lst,p]],{n,8!}];lst
Transpose[Select[Table[{n,Prime[n]},{n,3100}],And@@PrimeQ[{Last[#]- First[#],Total[#]}]&]][[2]] (* Harvey P. Dale, Nov 04 2011 *)
  • PARI
    n=0;forprime(p=2,1e5,if(isprime(p-n++)&&isprime(p+n),print1(p", "))) \\ Charles R Greathouse IV, Nov 04 2011

Extensions

Definition edited by Harvey P. Dale, Nov 04 2011

A112529 Numbers n such that prime(n) +/- 2n are both primes.

Original entry on oeis.org

7, 9, 12, 24, 30, 36, 63, 90, 102, 117, 126, 135, 150, 156, 165, 171, 180, 183, 225, 234, 270, 285, 369, 390, 399, 402, 447, 456, 501, 507, 537, 570, 582, 624, 627, 642, 651, 654, 660, 720, 735, 762, 777, 855, 864, 870, 885, 930, 936, 945, 1023, 1029, 1035
Offset: 1

Views

Author

Zak Seidov, Sep 10 2005

Keywords

Comments

Cf. A064403: Prime(n) +/- n are both primes

Crossrefs

Cf. A064403.

Programs

  • Mathematica
    Select[Range[2000], PrimeQ[Prime[ # ]+2# ]&&PrimeQ[Prime[ # ]-2# ]&]

A113567 Numbers n such that prime(n) +- n, prime(n) +- 2n and prime(n) +- 3n are all primes.

Original entry on oeis.org

252420, 874650, 1413510, 2053380, 2298240, 2456160, 4640370, 7529340, 8708910, 11205390, 18734310, 22141980, 23680650, 26407920, 30866010, 31340400, 38515050, 43242780, 44584260, 58430400, 61172790, 62739180, 64449210
Offset: 1

Views

Author

Robert G. Wilson v, Sep 20 2005

Keywords

Crossrefs

Cf. A064403, A112530.

Programs

  • Mathematica
    t = {}; p = 2*3*5*7; Do[ If[ PrimeQ[Prime[p*n] - p*3n] && PrimeQ[Prime[p*n] - p*2n] && PrimeQ[Prime[p*n] - p*n] && PrimeQ[Prime[p*n] + p*n] && PrimeQ[Prime[p*n] + p*2n] && PrimeQ[Prime[p*n] + p*3n], AppendTo[t, n]], {n, 2194723}]; p*t

A105550 Numbers n such that n/6 and prime(n)+/-n are all primes.

Original entry on oeis.org

18, 42, 66, 282, 618, 1374, 1698, 2022, 2766, 2778, 2874, 3594, 3918, 5718, 6918, 7734, 9138, 9582, 9726, 10806, 11334, 11442, 14226, 14394, 14802, 15306, 16386, 17994, 20226, 20334, 21954, 25374, 27366, 27822
Offset: 1

Views

Author

Zak Seidov, May 03 2005

Keywords

Links

Crossrefs

Cf. A064403.

Programs

  • Mathematica
    Select[Range[6,30000,6],AllTrue[{#/6,Prime[#]+#,Prime[#]-#},PrimeQ]&] (* Harvey P. Dale, Jan 14 2020 *)

A107636 Lesser prime in pair prime(k) +/- k for some k.

Original entry on oeis.org

3, 7, 43, 139, 251, 683, 1549, 2273, 2393, 2731, 3217, 3529, 3943, 4339, 4723, 4799, 4909, 5531, 5801, 7907, 9421, 10009, 11549, 12263, 12791, 13441, 14011, 14683, 15559, 18089, 19087, 20921, 22271, 22391, 23279, 24001, 24107, 24767, 24809, 26681, 26861, 27793
Offset: 1

Views

Author

Zak Seidov, May 19 2005

Keywords

Examples

			a(1) = 3 because A064403(1) = 4 and prime(4) - 4 = 7 - 4 = 3.

Crossrefs

Cf. A064403 (values of k), A107637, A143794 (prime(k)).

Programs

  • Mathematica
    R=3000;L=Select[Range[R], AllTrue[Prime[#]+{#, -#}, PrimeQ]&];Prime/@L-L (* James C. McMahon, Feb 18 2024 *)

Formula

a(n) = prime(A064403(n)) - A064403(n).

A107637 Larger prime in pair prime(k) +/- k for some k.

Original entry on oeis.org

11, 19, 79, 223, 383, 971, 2113, 3041, 3209, 3631, 4261, 4657, 5179, 5683, 6163, 6263, 6397, 7187, 7517, 10151, 12037, 12757, 14669, 15551, 16187, 16993, 17707, 18523, 19603, 22697, 23911, 26153, 27803, 27947, 29027, 29917, 30047, 30839, 30893, 33161, 33377
Offset: 1

Views

Author

Zak Seidov, May 19 2005

Keywords

Examples

			Prime 11 is a term because 11 = prime(4)+4 and 3 = prime(4)-4 is also a prime.

Crossrefs

Cf. A064403 (values of k), A107636 (prime(k)-k), A143794 (prime(k)).

Programs

  • Mathematica
    R=3000; L=Select[Range[R], AllTrue[Prime[#]+{#, -#}, PrimeQ]&]; Prime/@L+L (* James C. McMahon, Feb 18 2024 *)

Formula

a(n) = prime(A064403(n)) + A064403(n).

A113568 Numbers k such that prime(k) +- k, prime(k) +- 2k, prime(k) +- 3k and prime(k) +- 4k are all primes.

Original entry on oeis.org

2053380, 794006430, 1659273630, 3621510480, 3725013180, 4361365470, 4993201710, 7311363150, 7865614680, 9934880340, 10608361260, 12818200500, 13499311980, 13940598420, 14241904320, 14463052170, 14601895770, 18668815620, 19102545000, 20336611050, 20706006090, 21322649670, 22595831580
Offset: 1

Views

Author

Robert G. Wilson v, Sep 20 2005

Keywords

Crossrefs

Cf. A064403, A112530, A113567.

Programs

  • Mathematica
    t = {}; p = 2*3*5*7; Do[ If[ PrimeQ[Prime[p*n] - p*3n] && PrimeQ[Prime[p*n] - p*2n] && PrimeQ[Prime[p*n] - p*n] && PrimeQ[Prime[p*n] + p*n] && PrimeQ[Prime[p*n] + p*2n] && PrimeQ[Prime[p*n] + p*3n], AppendTo[t, n]], {n, 17 106}]; p*t
  • PARI
    list(lim) = {my(k = 0, q); forprime(p = 1, lim, k++; q = 1; for(i = -4, 4, if(i != 0 && !isprime(p + i*k), q = 0; break)); if(q, print1(k,", ")));} \\ Amiram Eldar, Jul 12 2025

Extensions

a(4)-a(23) from Amiram Eldar, Jul 12 2025

A113569 Least number k such that k is a multiple of A034386(2*n) and p-(n-1)*k, p-(n-2)*k, ... p-2*k, p-k, p, p+k, p+2*k, ... p+(n-2)*k, and p+(n-1)*k are all prime, with p being the k-th prime.

Original entry on oeis.org

2, 6, 720, 252420, 2053380
Offset: 1

Views

Author

Robert G. Wilson v, Sep 10 2005

Keywords

Comments

Without the condition that k must be a multiple of A034386(2*n), we would have a(1) = 1 and a(2) = 4. - Pontus von Brömssen, Jun 25 2025

Examples

			a(1) = 2 which is a multiple of the primorial A034386(2) = 2.
a(2) = 6 because p = 13, p-6 = 7, and p+6 = 19 are all prime and 6 is a multiple of A034386(4) = 6.
a(3) = 720 because p = 5443, p-720 = 4723, p-2*720 = 4003, p+720 = 6163, and p+2*720 = 6883 are all prime and 720 is a multiple of A034386(6) = 30.

Crossrefs

Cf. A034386, A064403, A112530, A113567, A113568.

Extensions

Edited by Pontus von Brömssen, Jun 25 2025
Showing 1-9 of 9 results.

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